Solve each of the following equations. Show its solution set on the number line. |3x-4(x+1)|=2

In a swim-and-run biathlon, An Athlete must get to a point on the other side of a 50 meter wide river, 100 meters downstream fro

ludmilkaskok [199]

Answer:

running distance = 78,18 m

swimmingdistance = 92m

Step-by-step explanation:

Ann has to run a distance 100 - x and swim √ (50)² + x²

at speed of 5 m/sec and 2 m/sec

As distance = v*t t = d/v

Then running she will spend time doing d = ( 100-x)/5

and √[(50)² + x² ] / 2 swimming

Therefore total time of biathlon

t(x) = ( 100 - x )/5 + √[(50)² + x² ] / 2

Taking derivatives both sides of the equation we get

t´(x) = - 1/5 + [1/2 ( 2x)*2] / 4√[(50)² + x²]

t´(x) = - 1/5 + 2x / 4√[(50)² + x²] t´(x) = - 1/5 + x/2√(50)² + x²

t´(x) = 0 - 1/5 + x/2√(50)² + x² = 0

- 2√[(50)²+ x²] + 5x = 0

- 2√(50)²+ x² ) = -5x

√(50)²+ x² = 5/2 *x

squared

(50)² + x² = 25/4 x²

2500 - 21/4 x² = 0

x² = 2500*4/21

x = 21,8 m

Therefore she has to run 100 - 21,82 = 78,18 m

And swim √(50)² + (78,18)² = 92m

5 0

3 years ago

You pack sandwiches for a mountain hike with your friends. each sandwich takes 2 slices of bread, and you pack 3 sandwiches for

Brrunno [24]

2*3n would be the equation.

6 0

3 years ago

Plz hurry!!!! thank you!!!!

RoseWind [281]

Answer:

$m\angle KLM=53.13^o$

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the measure of angle KOM

In the triangle KOM

we have

$KO=MO=r=5\ units$

$KM=8\ units$

Applying the law of cosines

$8^2=5^2+5^2-2(5)(5)cos(KOM)$

$64=50-50cos(KOM)$

$50cos(KOM)=50-64$

$50cos(KOM)=-14$

$cos(KOM)=-14/50$

$m\angle KOM=cos^{-1}(-14/50)$

$m\angle KOM=106.26^o$

step 2

Find the measure of the arc KM

we know that

$arc\ KM=m\angle KOM$ ----> by central angle

we have

$m\angle KOM=106.26^o$

so

$arc\ KM=106.26^o$

step 3

Find the measure of angle KLM

we know that

The inscribed angle is half that of the arc comprising

$m\angle KLM=\frac{1}{2}[arc\ KM]$

we have

$arc\ KM=106.26^o$

substitute

$m\angle KLM=\frac{1}{2}[106.26^o]$

$m\angle KLM=53.13^o$

7 0

3 years ago

Meg lives in Indianapolis and wants to visit her mom in Lima. She has been meaning to go to a chiropractor in Dayton, so she is

ella [17]

Answer: 44 miles

WORKINGS

Given,
The distance between Indianapolis and Lima, IL = 173 miles
The distance between Indianapolis and Dayton, ID = 165 miles
The distance between Dayton and Lima, DL is unknown

Since there are straight roads connecting the three cities, the connection between them form a right angles triangle.

The right angle is at Dayton
The hypotenuse is the distance between Indianapolis and Lima, IL

Therefore IL^2 = ID^2 + DL^2
173^2 = 165^2 + DL^2
DL^2 = 173^2 – 165^2
DL^2 = 29929 – 27225
DL^2 = 2704
DL = 52 miles

Therefore, The distance between Dayton and Lima, DL = 52 miles

The question is asking how many more miles would Meg drive if she stopped in Dayton first than if she drove directly to Lima.

That is, Distance of Indianapolis to Dayton + Distance of Dayton to Lima – Direct distance of Indianapolis to Lima
That is, ID + DL – IL
= 165 miles + 52 miles – 173 miles
= 217 miles – 173 miles
= 44 miles

Therefore, Meg would drive 44 more miles if she stopped in Dayton first than if she drove directly to Lima.

7 0

2 years ago

F(x) =6x-1<br> The equation represents Function a and the graph represents b

MAVERICK [17]

Answer:

Step-by-step explanation: ok

8 0

3 years ago